Related papers: Fractional Vector Calculus and Fractional Maxwell'…
Fractional derivatives are nonlocal differential operators of real order that often appear in models of anomalous diffusion and a variety of nonlocal phenomena. Recently, a version of the Schr\"odinger Equation containing a fractional…
In this paper we discuss fractional generalizations of the filtering problem. The "fractional" nature comes from time-changed state or observation processes, basic ingredients of the filtering problem. The mathematical feature of the…
We prove Euler-Lagrange fractional equations and sufficient optimality conditions for problems of the calculus of variations with functionals containing both fractional derivatives and fractional integrals in the sense of Riemann-Liouville.
Fractional calculus is an effective tool in incorporating the effects of non-locality and memory into physical models. In this regard, successful applications exist rang- ing from signal processing to anomalous diffusion and quantum…
A theory of time and space with fractional dimensions (FD) of time and space ($d_{\alpha}, \alpha=t,{\bf r})$ defined on multifractal sets is proposed. The FD is determined (using principle of minimum the functionals of FD) by the energy…
Local fractional derivative and integrals are revealed as one of useful tools to deal with everywhere continuous but nowhere differentiable functions in fractal areas ranging from fundamental science to engineering. In this paper, a…
The goal of this work is to discuss how should we impose initial values in fractional problems to ensure that they have exactly one smooth unique solution, where smooth simply means that the solution lies in a certain suitable space of…
In this work we look at the original fractional calculus of variations problem in a somewhat different way. As a simple consequence, we show that a fractional generalization of a classical problem has a solution without any restrictions on…
In a recent paper, Cohl and Costas-Santos derived a number of interesting multi-derivative and multi-integral relations for associated Legendre and Ferrers functions in which the orders of those functions are changed in integral steps.…
In this note, a numerical method based on finite differences to solve a class of nonlinear advection-diffusion fractional differential equation is proposed. The fractional operator considered here is the fractional Riemann-Liouville…
There are many research available on the study of real-valued fractal interpolation function and fractal dimension of its graph. In this paper, our main focus is to study the dimensional results for vector-valued fractal interpolation…
The thesis deals with applications of fractional calculus to fractals. It introduces the notion of local fractional derivative (LFD). Fractal and multifractal functions have been studied in the thesis using LFD. New kind of equations are…
In this paper, we present the definitions and some properties of the general fractional integrals (GFIs) and general fractional derivatives (GFDs) of a function f(x) with respect to another function g(x). Examples of special cases of…
This paper presents a modified numerical scheme for a class of Fractional Optimal Control Problems (FOCPs) formulated in Agrawal (2004) where a Fractional Derivative (FD) is defined in the Riemann-Liouville sense. In this scheme, the entire…
The paper discusses the characteristic properties of fractional derivatives of non-integer order. It is known that derivatives of integer orders are determined by properties of differentiable functions only in an infinitely small…
We presented a general approach for obtaining the generalized transport equations with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and Zubarev's nonequilibrium…
The fractional calculus is useful to model non-local phenomena. We construct a method to evaluate the fractional Caputo derivative by means of a simple explicit quadratic segmentary interpolation. This method yields to numerical resolution…
This manuscript is dedicated to prove a new inequality that involves an important case of Leibniz rule regarding Riemann-Liouville and Caputo fractional derivatives of order $\alpha\in(0,1)$. In the context of partial differential…
Fractional calculus has become widely studied and applied to physical problems in recent years. As a result, many methods for the numerical computation of fractional derivatives and integrals have been defined. However, these algorithms are…
This paper presents the Euler-Lagrange equations for fractional variational problems with multiple integrals. The fractional Noether-type theorem for conservative and nonconservative generalized physical systems is proved. Our approach uses…